scholarly journals Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 451
Author(s):  
Hayrinisa Demirci Biçer
Keyword(s):  
Statistical Inference ◽  
Arrival Time ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Arrival Times ◽  
Generalized Rayleigh Distribution ◽  
First Arrival ◽  
L Moments ◽  
Monotone Trend ◽  
First Arrival Time

In the modeling of successive arrival times with a monotone trend, the alpha-series process provides quite successful results. Both selecting the distribution of the first arrival time and making an optimal statistical inference play a crucial role in the modeling performance of the alpha-series process. In this study, when the distribution of the first arrival time is the generalized Rayleigh, the problem of statistical inference for the α , β , and λ parameters of the alpha-series process is considered. Further, in order to obtain optimal modeling performance from the mentioned alpha-series process, various estimators for the model parameters are obtained by employing different estimation methodologies such as maximum likelihood, modified maximum spacing, modified least-squares, modified moments, and modified L-moments. By a series of Monte Carlo simulations, the estimation efficiencies of the obtained estimators are evaluated through the different sample sizes. Finally, two real datasets are analyzed to illustrate the importance of modeling with the alpha-series process.

scholarly journals STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE GENERALIZED RAYLEIGH DISTRIBUTION

2021 ◽  
pp. 1107
Author(s):  
Cenker Biçer ◽  
Hayrinisa D. Biçer ◽  
Mahmut Kara ◽  
Asuman Yılmaz
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Inference Problem ◽  
Geometric Process ◽  
Generalized Rayleigh Distribution ◽  
First Arrival ◽  
Modeling Behavior

In the present paper, statistical inference problem is considered for the geometric process (GP) by assuming the distribution of the first arrival time is generalized Rayleigh with the parameters $\alpha$ and $\lambda$. We use the maximum likelihood method for obtaining the ratio parameter of the GP and distributional parameters of the generalized Rayleigh distribution. By a series of Monte-Carlo simulations evaluated through the different samples of sizes small, moderate and large, we also compare the estimation performances of the maximum likelihood estimators with the other estimators available in the literature such as modified moment, modified L-moment, and modified least squares. Furthermore, we present two real-life dataset analyzes to show the modeling behavior of GP with generalized Rayleigh distribution.

First arrival time picking for microseismic data based on DWSW algorithm

2018 ◽  
Vol 22 (4) ◽  
pp. 833-840 ◽  
Author(s):  
Yue Li ◽  
Yue Wang ◽  
Hongbo Lin ◽  
Tie Zhong
Keyword(s):  
Arrival Time ◽  
Microseismic Data ◽  
First Arrival ◽  
First Arrival Time ◽  
Arrival Time Picking

scholarly journals ANALYSES OF THE AGE OF GENES AND THE FIRST ARRIVAL TIMES IN A FINITE POPULATION

Genetics ◽  
1983 ◽  
Vol 105 (4) ◽  
pp. 1041-1059
Author(s):  
Takeo Maruyama ◽  
Paul A Fuerst
Keyword(s):  
Arrival Time ◽  
Mutant Gene ◽  
Intermediate Frequency ◽  
Lag Phase ◽  
Reversal Theory ◽  
Infinite Allele Model ◽  
First Arrival ◽  
Mean And Variance ◽  
The Mean ◽  
First Arrival Time

ABSTRACT The age of a mutant gene is studied using the infinite allele model in which every mutant is new and selectively neutral. Based on a time reversal theory of Markov processes, we develop a method of mathematical analysis that is considerably simpler for calculating the various statistics of the age than previous methods. Formulas for the mean and variance and for the distribution of age are presented together with some examples of relevance to cases in natural populations.—Theoretical studies of the first arrival time of an allele to a specified frequency, given an initially monomorphic condition of the locus, are presented. It is shown that, beginning with an allele that has frequency p = 1 or an allele with frequency p = 1/2N, there is an initial lag phase in which there is virtually no chance of an allele with a specified intermediate frequency appearing in the population. The distribution of the first arrival time is also presented. The distribution shows several characteristics that are not immediately obvious from a consideration of only the mean and variance of first arrival time. Especially noteworthy is the existence of a very long tail to the distribution. We have also studied the distribution of the age of an allele in the population. Again, the distribution of this measure is shown to be more informative for several questions than are the mean and variance alone.

scholarly journals Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 449 ◽  
Author(s):  
Abdullah M. Almarashi ◽  
Majdah M. Badr ◽  
Mohammed Elgarhy ◽  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Statistical Inference ◽  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Linear Representation ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
New Model ◽  
Entropy Measures ◽  
Lifetime Studies

The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.

scholarly journals Modeling across-trial variability in the Wald drift rate parameter

2020 ◽  
Author(s):  
Helen Steingroever ◽  
Dominik Wabersich ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Drift Rate ◽  
Model Parameters ◽  
Analysis Tool ◽  
Rate Parameter ◽  
Data Set ◽  
Arrival Times ◽  
First Arrival ◽  
Truncated Normal ◽  
Experimental Trials ◽  
Variance Parameter

Abstract The shifted-Wald model is a popular analysis tool for one-choice reaction-time tasks. In its simplest version, the shifted-Wald model assumes a constant trial-independent drift rate parameter. However, the presence of endogenous processes—fluctuation in attention and motivation, fatigue and boredom—suggest that drift rate might vary across experimental trials. Here we show how across-trial variability in drift rate can be accounted for by assuming a trial-specific drift rate parameter that is governed by a positive-valued distribution. We consider two candidate distributions: the truncated normal distribution and the gamma distribution. For the resulting distributions of first-arrival times, we derive analytical and sampling-based solutions, and implement the models in a Bayesian framework. Recovery studies and an application to a data set comprised of 1469 participants suggest that (1) both mixture distributions yield similar results; (2) all model parameters can be recovered accurately except for the drift variance parameter; (3) despite poor recovery, the presence of the drift variance parameter facilitates accurate recovery of the remaining parameters; (4) shift, threshold, and drift mean parameters are correlated.

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